In [1]}, the authors prove several bounds on the average path length in a random graph \(G(n,p)\) . In particular, they state that if \(np \ge c > 1\) , then the average distance is constant times \(\frac{\log {n}}{\log {np}}\) . Using this result, we assume that the average distance between two vertices in subgraph \(S_k\)  is \(\frac{\log {n_k}}{\log {n_kp_k}} \approx \frac{\log {n_k}}{\log {d_k}}\) .
